Abstract

We have studied surface defect gap solitons in an interface between a defect of one-dimensional (1D) chirped optical lattices (OLs) and uniform Kerr-type nonlinear media. Some unique properties are revealed due to the competition between the defect and the chirp. It was interestingly found that a positive defect facilitates the generation of surface solitons in the negatively chirped OLs, while a negative defect destroys surface solitons in the positively chirped OLs. These phenomena are different from previous results in both the positively and negatively chirped OLs without defect. The band spectrum and stable domains are analyzed in detail.

© 2010 Optical Society of America

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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  6. Y. V. Kartashov and L. Torner, “Multipole-mode surface solitons,” Opt. Lett. 31, 2172-2174 (2006).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  13. K. Motzek, A. A. Sukhorukov, and Y. S. Kivshar, “Self-trapping of polychromatic light in nonlinear periodic photonic structures,” Opt. Express 14, 9873-9878 (2006).
    [CrossRef] [PubMed]
  14. K. Motzek, A. A. Sukhorukov, and Y. S. Kivshar, “Polychromatic interface solitons in nonlinear photonic lattices,” Opt. Lett. 31, 3125-3127 (2006).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
  25. D. Mihalache, D. Mazilu, F. Lederer, and Y. S. Kivshar, “Spatiotemporal surface solitons in two-dimensional photonic lattices,” Opt. Lett. 32, 3173-3175 (2007).
    [CrossRef] [PubMed]
  26. Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Dynamics of surface solitons at the edge of chirped optical lattices,” Phys. Rev. A 76, 013831 (2007).
    [CrossRef]
  27. A. A. Sukhorukov and Y. S. Kivshar, “Nonlinear localized waves in a periodic medium,” Phys. Rev. Lett. 87, 083901 (2001).
    [CrossRef] [PubMed]
  28. J. Yang and Z. Chen, “Defect solitons in photonic lattices,” Phys. Rev. E 73, 026609 (2006).
    [CrossRef]
  29. W. H. Chen, Y. J. He, and H. Z. Wang, “Surface defect gap solitons,” Opt. Express 14, 11271-11276 (2006).
    [CrossRef] [PubMed]
  30. W. L. Zhu, L. Luo, and Y. J. He, “Surface gap solitons in one-dimensional dual-frequency lattices,” J. Mod. Opt. 56, 1078-1082 (2009).
    [CrossRef]

2009 (1)

W. L. Zhu, L. Luo, and Y. J. He, “Surface gap solitons in one-dimensional dual-frequency lattices,” J. Mod. Opt. 56, 1078-1082 (2009).
[CrossRef]

2007 (9)

H. Susanto, P. G. Kevrekidis, B. A. Malomed, R. Carretero-González, and D. J. Frantzeskakis, “Discrete surface solitons in two dimensions,” Phys. Rev. E 75, 056605 (2007).
[CrossRef]

D. Mihalache, D. Mazilu, F. Lederer, and Y. S. Kivshar, “Stable discrete surface light bullets,” Opt. Express 15, 589-595 (2007).
[CrossRef] [PubMed]

M. Stepić, E. Smirnov, C. E. Rüter, D. Kip, A. Maluckov, and L. Hadžievski, “Tamm oscillations in semi-infinite nonlinear waveguide arrays,” Opt. Lett. 32, 823-825 (2007).
[CrossRef]

Y. J. He, W. H. Chen, H. Z. Wang, and B. A. Malomed, “Surface superlattices gap solitons,” Opt. Lett. 32, 1390-1392 (2007).
[CrossRef] [PubMed]

S. Suntsov, K. G. Makris, D. N. Christodoulides, G. I. Stegeman, R. Morandotti, H. Yang, G. Salamo, and M. Sorel, “Power thresholds of families of discrete surface solitons,” Opt. Lett. 32, 3098-3100 (2007).
[CrossRef] [PubMed]

D. Mihalache, D. Mazilu, F. Lederer, and Y. S. Kivshar, “Spatiotemporal surface solitons in two-dimensional photonic lattices,” Opt. Lett. 32, 3173-3175 (2007).
[CrossRef] [PubMed]

X. Wang, A. Bezryadina, Z. Chen, K. G. Makris, D. N. Christodoulides, and G. I. Stegeman, “Observation of two-dimensional surface solitons,” Phys. Rev. Lett. 98, 123903 (2007).
[CrossRef] [PubMed]

A. Szameit, Y. V. Kartashov, F. Dreisow, T. Pertsch, S. Nolte, A. Tunnermann, and L. Torner, “Observation of two-dimensional surface solitons in asymmetric waveguide arrays,” Phys. Rev. Lett. 98, 173903 (2007).
[CrossRef]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Dynamics of surface solitons at the edge of chirped optical lattices,” Phys. Rev. A 76, 013831 (2007).
[CrossRef]

2006 (18)

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Surface gap solitons,” Phys. Rev. Lett. 96, 073901 (2006).
[CrossRef] [PubMed]

C. R. Rosberg, D. N. Neshev, W. Krolikowski, A. Mitchell, R. A. Vicencio, M. I. Molina, and Y. S. Kivshar, “Observation of surface gap solitons in semi-infinite waveguide arrays,” Phys. Rev. Lett. 97, 083901 (2006).
[CrossRef] [PubMed]

J. Yang and Z. Chen, “Defect solitons in photonic lattices,” Phys. Rev. E 73, 026609 (2006).
[CrossRef]

S. Suntsov, K. G. Makris, D. N. Christodoulides, G. I. Stegeman, A. Hache, R. Morandotti, H. Yang, G. Salamo, and M. Sorel, “Observation of discrete surface solitons,” Phys. Rev. Lett. 96, 063901 (2006).
[CrossRef] [PubMed]

Y. V. Kartashov, A. A. Egorov, V. A. Vysloukh, and L. Torner, “Surface vortex solitons,” Opt. Express 14, 4049-4057 (2006).
[CrossRef] [PubMed]

M. I. Molina, R. A. Vicencio, and Y. S. Kivshar, “Discrete solitons and nonlinear surface modes in semi-infinite waveguide arrays,” Opt. Lett. 31, 1693-1695 (2006).
[CrossRef] [PubMed]

I. L. Garanovich, A. A. Sukhorukov, and Y. S. Kivshar, “Surface multi-gap vector solitons,” Opt. Express 14, 4780-4785 (2006).
[CrossRef] [PubMed]

Y. V. Kartashov, F. Ye, and L. Torner, “Vector mixed-gap surface solitons,” Opt. Express 14, 4808-4814 (2006).
[CrossRef] [PubMed]

Y. V. Kartashov and L. Torner, “Multipole-mode surface solitons,” Opt. Lett. 31, 2172-2174 (2006).
[CrossRef] [PubMed]

Y. V. Kartashov, V. A. Vysloukh, D. Mihalache, and L. Torner, “Generation of surface soliton arrays,” Opt. Lett. 31, 2329-2331 (2006).
[CrossRef] [PubMed]

M. I. Molina, I. L. Garanovich, A. A. Sukhorukov, and Y. S. Kivshar, “Discrete surface solitons in semi-infinite binary waveguide arrays,” Opt. Lett. 31, 2332-2334 (2006).
[CrossRef] [PubMed]

E. Smirnov, M. Stepić, C. E. Rüter, D. Kip, and V. Shandarov, “Observation of staggered surface solitary waves in one-dimensional waveguide arrays,” Opt. Lett. 31, 2338-2340 (2006).
[CrossRef] [PubMed]

K. G. Makris, J. Hudock, D. N. Christodoulides, G. I. Stegeman, O. Manela, and M. Segev, “Surface lattice solitons,” Opt. Lett. 31, 2774-2776 (2006).
[CrossRef] [PubMed]

K. Motzek, A. A. Sukhorukov, and Y. S. Kivshar, “Polychromatic interface solitons in nonlinear photonic lattices,” Opt. Lett. 31, 3125-3127 (2006).
[CrossRef] [PubMed]

K. Motzek, A. A. Sukhorukov, and Y. S. Kivshar, “Self-trapping of polychromatic light in nonlinear periodic photonic structures,” Opt. Express 14, 9873-9878 (2006).
[CrossRef] [PubMed]

A. A. Sukhorukov, D. N. Neshev, A. Dreischuh, R. Fischer, S. Ha, W. Krolikowski, J. Bolger, A. Mitchell, B. J. Eggleton, and Y. S. Kivshar, “Polychromatic nonlinear surface modes generated by supercontinuum light,” Opt. Express 14, 11265-11270 (2006).
[CrossRef] [PubMed]

W. H. Chen, Y. J. He, and H. Z. Wang, “Surface defect gap solitons,” Opt. Express 14, 11271-11276 (2006).
[CrossRef] [PubMed]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Surface lattice kink solitons,” Opt. Express 14, 12365-12372 (2006).
[CrossRef] [PubMed]

2005 (1)

2001 (1)

A. A. Sukhorukov and Y. S. Kivshar, “Nonlinear localized waves in a periodic medium,” Phys. Rev. Lett. 87, 083901 (2001).
[CrossRef] [PubMed]

Bezryadina, A.

X. Wang, A. Bezryadina, Z. Chen, K. G. Makris, D. N. Christodoulides, and G. I. Stegeman, “Observation of two-dimensional surface solitons,” Phys. Rev. Lett. 98, 123903 (2007).
[CrossRef] [PubMed]

Bolger, J.

Carretero-González, R.

H. Susanto, P. G. Kevrekidis, B. A. Malomed, R. Carretero-González, and D. J. Frantzeskakis, “Discrete surface solitons in two dimensions,” Phys. Rev. E 75, 056605 (2007).
[CrossRef]

Chen, W. H.

Chen, Z.

X. Wang, A. Bezryadina, Z. Chen, K. G. Makris, D. N. Christodoulides, and G. I. Stegeman, “Observation of two-dimensional surface solitons,” Phys. Rev. Lett. 98, 123903 (2007).
[CrossRef] [PubMed]

J. Yang and Z. Chen, “Defect solitons in photonic lattices,” Phys. Rev. E 73, 026609 (2006).
[CrossRef]

Christodoulides, D. N.

Dreischuh, A.

Dreisow, F.

A. Szameit, Y. V. Kartashov, F. Dreisow, T. Pertsch, S. Nolte, A. Tunnermann, and L. Torner, “Observation of two-dimensional surface solitons in asymmetric waveguide arrays,” Phys. Rev. Lett. 98, 173903 (2007).
[CrossRef]

Eggleton, B. J.

Egorov, A. A.

Fischer, R.

Frantzeskakis, D. J.

H. Susanto, P. G. Kevrekidis, B. A. Malomed, R. Carretero-González, and D. J. Frantzeskakis, “Discrete surface solitons in two dimensions,” Phys. Rev. E 75, 056605 (2007).
[CrossRef]

Garanovich, I. L.

Ha, S.

Hache, A.

S. Suntsov, K. G. Makris, D. N. Christodoulides, G. I. Stegeman, A. Hache, R. Morandotti, H. Yang, G. Salamo, and M. Sorel, “Observation of discrete surface solitons,” Phys. Rev. Lett. 96, 063901 (2006).
[CrossRef] [PubMed]

Hadžievski, L.

He, Y. J.

Hudock, J.

Kartashov, Y. V.

Kevrekidis, P. G.

H. Susanto, P. G. Kevrekidis, B. A. Malomed, R. Carretero-González, and D. J. Frantzeskakis, “Discrete surface solitons in two dimensions,” Phys. Rev. E 75, 056605 (2007).
[CrossRef]

Kip, D.

Kivshar, Y. S.

D. Mihalache, D. Mazilu, F. Lederer, and Y. S. Kivshar, “Stable discrete surface light bullets,” Opt. Express 15, 589-595 (2007).
[CrossRef] [PubMed]

D. Mihalache, D. Mazilu, F. Lederer, and Y. S. Kivshar, “Spatiotemporal surface solitons in two-dimensional photonic lattices,” Opt. Lett. 32, 3173-3175 (2007).
[CrossRef] [PubMed]

M. I. Molina, I. L. Garanovich, A. A. Sukhorukov, and Y. S. Kivshar, “Discrete surface solitons in semi-infinite binary waveguide arrays,” Opt. Lett. 31, 2332-2334 (2006).
[CrossRef] [PubMed]

A. A. Sukhorukov, D. N. Neshev, A. Dreischuh, R. Fischer, S. Ha, W. Krolikowski, J. Bolger, A. Mitchell, B. J. Eggleton, and Y. S. Kivshar, “Polychromatic nonlinear surface modes generated by supercontinuum light,” Opt. Express 14, 11265-11270 (2006).
[CrossRef] [PubMed]

K. Motzek, A. A. Sukhorukov, and Y. S. Kivshar, “Polychromatic interface solitons in nonlinear photonic lattices,” Opt. Lett. 31, 3125-3127 (2006).
[CrossRef] [PubMed]

I. L. Garanovich, A. A. Sukhorukov, and Y. S. Kivshar, “Surface multi-gap vector solitons,” Opt. Express 14, 4780-4785 (2006).
[CrossRef] [PubMed]

M. I. Molina, R. A. Vicencio, and Y. S. Kivshar, “Discrete solitons and nonlinear surface modes in semi-infinite waveguide arrays,” Opt. Lett. 31, 1693-1695 (2006).
[CrossRef] [PubMed]

C. R. Rosberg, D. N. Neshev, W. Krolikowski, A. Mitchell, R. A. Vicencio, M. I. Molina, and Y. S. Kivshar, “Observation of surface gap solitons in semi-infinite waveguide arrays,” Phys. Rev. Lett. 97, 083901 (2006).
[CrossRef] [PubMed]

K. Motzek, A. A. Sukhorukov, and Y. S. Kivshar, “Self-trapping of polychromatic light in nonlinear periodic photonic structures,” Opt. Express 14, 9873-9878 (2006).
[CrossRef] [PubMed]

A. A. Sukhorukov and Y. S. Kivshar, “Nonlinear localized waves in a periodic medium,” Phys. Rev. Lett. 87, 083901 (2001).
[CrossRef] [PubMed]

Krolikowski, W.

C. R. Rosberg, D. N. Neshev, W. Krolikowski, A. Mitchell, R. A. Vicencio, M. I. Molina, and Y. S. Kivshar, “Observation of surface gap solitons in semi-infinite waveguide arrays,” Phys. Rev. Lett. 97, 083901 (2006).
[CrossRef] [PubMed]

A. A. Sukhorukov, D. N. Neshev, A. Dreischuh, R. Fischer, S. Ha, W. Krolikowski, J. Bolger, A. Mitchell, B. J. Eggleton, and Y. S. Kivshar, “Polychromatic nonlinear surface modes generated by supercontinuum light,” Opt. Express 14, 11265-11270 (2006).
[CrossRef] [PubMed]

Lederer, F.

Luo, L.

W. L. Zhu, L. Luo, and Y. J. He, “Surface gap solitons in one-dimensional dual-frequency lattices,” J. Mod. Opt. 56, 1078-1082 (2009).
[CrossRef]

Makris, K. G.

Malomed, B. A.

Y. J. He, W. H. Chen, H. Z. Wang, and B. A. Malomed, “Surface superlattices gap solitons,” Opt. Lett. 32, 1390-1392 (2007).
[CrossRef] [PubMed]

H. Susanto, P. G. Kevrekidis, B. A. Malomed, R. Carretero-González, and D. J. Frantzeskakis, “Discrete surface solitons in two dimensions,” Phys. Rev. E 75, 056605 (2007).
[CrossRef]

Maluckov, A.

Manela, O.

Mazilu, D.

Mihalache, D.

Mitchell, A.

C. R. Rosberg, D. N. Neshev, W. Krolikowski, A. Mitchell, R. A. Vicencio, M. I. Molina, and Y. S. Kivshar, “Observation of surface gap solitons in semi-infinite waveguide arrays,” Phys. Rev. Lett. 97, 083901 (2006).
[CrossRef] [PubMed]

A. A. Sukhorukov, D. N. Neshev, A. Dreischuh, R. Fischer, S. Ha, W. Krolikowski, J. Bolger, A. Mitchell, B. J. Eggleton, and Y. S. Kivshar, “Polychromatic nonlinear surface modes generated by supercontinuum light,” Opt. Express 14, 11265-11270 (2006).
[CrossRef] [PubMed]

Molina, M. I.

Morandotti, R.

S. Suntsov, K. G. Makris, D. N. Christodoulides, G. I. Stegeman, R. Morandotti, H. Yang, G. Salamo, and M. Sorel, “Power thresholds of families of discrete surface solitons,” Opt. Lett. 32, 3098-3100 (2007).
[CrossRef] [PubMed]

S. Suntsov, K. G. Makris, D. N. Christodoulides, G. I. Stegeman, A. Hache, R. Morandotti, H. Yang, G. Salamo, and M. Sorel, “Observation of discrete surface solitons,” Phys. Rev. Lett. 96, 063901 (2006).
[CrossRef] [PubMed]

Motzek, K.

Neshev, D. N.

C. R. Rosberg, D. N. Neshev, W. Krolikowski, A. Mitchell, R. A. Vicencio, M. I. Molina, and Y. S. Kivshar, “Observation of surface gap solitons in semi-infinite waveguide arrays,” Phys. Rev. Lett. 97, 083901 (2006).
[CrossRef] [PubMed]

A. A. Sukhorukov, D. N. Neshev, A. Dreischuh, R. Fischer, S. Ha, W. Krolikowski, J. Bolger, A. Mitchell, B. J. Eggleton, and Y. S. Kivshar, “Polychromatic nonlinear surface modes generated by supercontinuum light,” Opt. Express 14, 11265-11270 (2006).
[CrossRef] [PubMed]

Nolte, S.

A. Szameit, Y. V. Kartashov, F. Dreisow, T. Pertsch, S. Nolte, A. Tunnermann, and L. Torner, “Observation of two-dimensional surface solitons in asymmetric waveguide arrays,” Phys. Rev. Lett. 98, 173903 (2007).
[CrossRef]

Pertsch, T.

A. Szameit, Y. V. Kartashov, F. Dreisow, T. Pertsch, S. Nolte, A. Tunnermann, and L. Torner, “Observation of two-dimensional surface solitons in asymmetric waveguide arrays,” Phys. Rev. Lett. 98, 173903 (2007).
[CrossRef]

Rosberg, C. R.

C. R. Rosberg, D. N. Neshev, W. Krolikowski, A. Mitchell, R. A. Vicencio, M. I. Molina, and Y. S. Kivshar, “Observation of surface gap solitons in semi-infinite waveguide arrays,” Phys. Rev. Lett. 97, 083901 (2006).
[CrossRef] [PubMed]

Rüter, C. E.

Salamo, G.

S. Suntsov, K. G. Makris, D. N. Christodoulides, G. I. Stegeman, R. Morandotti, H. Yang, G. Salamo, and M. Sorel, “Power thresholds of families of discrete surface solitons,” Opt. Lett. 32, 3098-3100 (2007).
[CrossRef] [PubMed]

S. Suntsov, K. G. Makris, D. N. Christodoulides, G. I. Stegeman, A. Hache, R. Morandotti, H. Yang, G. Salamo, and M. Sorel, “Observation of discrete surface solitons,” Phys. Rev. Lett. 96, 063901 (2006).
[CrossRef] [PubMed]

Segev, M.

Shandarov, V.

Smirnov, E.

Sorel, M.

S. Suntsov, K. G. Makris, D. N. Christodoulides, G. I. Stegeman, R. Morandotti, H. Yang, G. Salamo, and M. Sorel, “Power thresholds of families of discrete surface solitons,” Opt. Lett. 32, 3098-3100 (2007).
[CrossRef] [PubMed]

S. Suntsov, K. G. Makris, D. N. Christodoulides, G. I. Stegeman, A. Hache, R. Morandotti, H. Yang, G. Salamo, and M. Sorel, “Observation of discrete surface solitons,” Phys. Rev. Lett. 96, 063901 (2006).
[CrossRef] [PubMed]

Stegeman, G. I.

Stepic, M.

Sukhorukov, A. A.

Suntsov, S.

Susanto, H.

H. Susanto, P. G. Kevrekidis, B. A. Malomed, R. Carretero-González, and D. J. Frantzeskakis, “Discrete surface solitons in two dimensions,” Phys. Rev. E 75, 056605 (2007).
[CrossRef]

Szameit, A.

A. Szameit, Y. V. Kartashov, F. Dreisow, T. Pertsch, S. Nolte, A. Tunnermann, and L. Torner, “Observation of two-dimensional surface solitons in asymmetric waveguide arrays,” Phys. Rev. Lett. 98, 173903 (2007).
[CrossRef]

Torner, L.

Tunnermann, A.

A. Szameit, Y. V. Kartashov, F. Dreisow, T. Pertsch, S. Nolte, A. Tunnermann, and L. Torner, “Observation of two-dimensional surface solitons in asymmetric waveguide arrays,” Phys. Rev. Lett. 98, 173903 (2007).
[CrossRef]

Vicencio, R. A.

M. I. Molina, R. A. Vicencio, and Y. S. Kivshar, “Discrete solitons and nonlinear surface modes in semi-infinite waveguide arrays,” Opt. Lett. 31, 1693-1695 (2006).
[CrossRef] [PubMed]

C. R. Rosberg, D. N. Neshev, W. Krolikowski, A. Mitchell, R. A. Vicencio, M. I. Molina, and Y. S. Kivshar, “Observation of surface gap solitons in semi-infinite waveguide arrays,” Phys. Rev. Lett. 97, 083901 (2006).
[CrossRef] [PubMed]

Vysloukh, V. A.

Wang, H. Z.

Wang, X.

X. Wang, A. Bezryadina, Z. Chen, K. G. Makris, D. N. Christodoulides, and G. I. Stegeman, “Observation of two-dimensional surface solitons,” Phys. Rev. Lett. 98, 123903 (2007).
[CrossRef] [PubMed]

Yang, H.

S. Suntsov, K. G. Makris, D. N. Christodoulides, G. I. Stegeman, R. Morandotti, H. Yang, G. Salamo, and M. Sorel, “Power thresholds of families of discrete surface solitons,” Opt. Lett. 32, 3098-3100 (2007).
[CrossRef] [PubMed]

S. Suntsov, K. G. Makris, D. N. Christodoulides, G. I. Stegeman, A. Hache, R. Morandotti, H. Yang, G. Salamo, and M. Sorel, “Observation of discrete surface solitons,” Phys. Rev. Lett. 96, 063901 (2006).
[CrossRef] [PubMed]

Yang, J.

J. Yang and Z. Chen, “Defect solitons in photonic lattices,” Phys. Rev. E 73, 026609 (2006).
[CrossRef]

Ye, F.

Zhu, W. L.

W. L. Zhu, L. Luo, and Y. J. He, “Surface gap solitons in one-dimensional dual-frequency lattices,” J. Mod. Opt. 56, 1078-1082 (2009).
[CrossRef]

J. Mod. Opt. (1)

W. L. Zhu, L. Luo, and Y. J. He, “Surface gap solitons in one-dimensional dual-frequency lattices,” J. Mod. Opt. 56, 1078-1082 (2009).
[CrossRef]

Opt. Express (8)

Opt. Lett. (12)

Y. V. Kartashov and L. Torner, “Multipole-mode surface solitons,” Opt. Lett. 31, 2172-2174 (2006).
[CrossRef] [PubMed]

Y. V. Kartashov, V. A. Vysloukh, D. Mihalache, and L. Torner, “Generation of surface soliton arrays,” Opt. Lett. 31, 2329-2331 (2006).
[CrossRef] [PubMed]

M. I. Molina, I. L. Garanovich, A. A. Sukhorukov, and Y. S. Kivshar, “Discrete surface solitons in semi-infinite binary waveguide arrays,” Opt. Lett. 31, 2332-2334 (2006).
[CrossRef] [PubMed]

E. Smirnov, M. Stepić, C. E. Rüter, D. Kip, and V. Shandarov, “Observation of staggered surface solitary waves in one-dimensional waveguide arrays,” Opt. Lett. 31, 2338-2340 (2006).
[CrossRef] [PubMed]

K. G. Makris, J. Hudock, D. N. Christodoulides, G. I. Stegeman, O. Manela, and M. Segev, “Surface lattice solitons,” Opt. Lett. 31, 2774-2776 (2006).
[CrossRef] [PubMed]

K. Motzek, A. A. Sukhorukov, and Y. S. Kivshar, “Polychromatic interface solitons in nonlinear photonic lattices,” Opt. Lett. 31, 3125-3127 (2006).
[CrossRef] [PubMed]

M. Stepić, E. Smirnov, C. E. Rüter, D. Kip, A. Maluckov, and L. Hadžievski, “Tamm oscillations in semi-infinite nonlinear waveguide arrays,” Opt. Lett. 32, 823-825 (2007).
[CrossRef]

Y. J. He, W. H. Chen, H. Z. Wang, and B. A. Malomed, “Surface superlattices gap solitons,” Opt. Lett. 32, 1390-1392 (2007).
[CrossRef] [PubMed]

S. Suntsov, K. G. Makris, D. N. Christodoulides, G. I. Stegeman, R. Morandotti, H. Yang, G. Salamo, and M. Sorel, “Power thresholds of families of discrete surface solitons,” Opt. Lett. 32, 3098-3100 (2007).
[CrossRef] [PubMed]

D. Mihalache, D. Mazilu, F. Lederer, and Y. S. Kivshar, “Spatiotemporal surface solitons in two-dimensional photonic lattices,” Opt. Lett. 32, 3173-3175 (2007).
[CrossRef] [PubMed]

M. I. Molina, R. A. Vicencio, and Y. S. Kivshar, “Discrete solitons and nonlinear surface modes in semi-infinite waveguide arrays,” Opt. Lett. 31, 1693-1695 (2006).
[CrossRef] [PubMed]

K. G. Makris, S. Suntsov, D. N. Christodoulides, and G. I. Stegeman, “Discrete surface solitons,” Opt. Lett. 30, 2466-2468 (2005).
[CrossRef] [PubMed]

Phys. Rev. A (1)

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Dynamics of surface solitons at the edge of chirped optical lattices,” Phys. Rev. A 76, 013831 (2007).
[CrossRef]

Phys. Rev. E (2)

J. Yang and Z. Chen, “Defect solitons in photonic lattices,” Phys. Rev. E 73, 026609 (2006).
[CrossRef]

H. Susanto, P. G. Kevrekidis, B. A. Malomed, R. Carretero-González, and D. J. Frantzeskakis, “Discrete surface solitons in two dimensions,” Phys. Rev. E 75, 056605 (2007).
[CrossRef]

Phys. Rev. Lett. (6)

S. Suntsov, K. G. Makris, D. N. Christodoulides, G. I. Stegeman, A. Hache, R. Morandotti, H. Yang, G. Salamo, and M. Sorel, “Observation of discrete surface solitons,” Phys. Rev. Lett. 96, 063901 (2006).
[CrossRef] [PubMed]

A. A. Sukhorukov and Y. S. Kivshar, “Nonlinear localized waves in a periodic medium,” Phys. Rev. Lett. 87, 083901 (2001).
[CrossRef] [PubMed]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Surface gap solitons,” Phys. Rev. Lett. 96, 073901 (2006).
[CrossRef] [PubMed]

C. R. Rosberg, D. N. Neshev, W. Krolikowski, A. Mitchell, R. A. Vicencio, M. I. Molina, and Y. S. Kivshar, “Observation of surface gap solitons in semi-infinite waveguide arrays,” Phys. Rev. Lett. 97, 083901 (2006).
[CrossRef] [PubMed]

X. Wang, A. Bezryadina, Z. Chen, K. G. Makris, D. N. Christodoulides, and G. I. Stegeman, “Observation of two-dimensional surface solitons,” Phys. Rev. Lett. 98, 123903 (2007).
[CrossRef] [PubMed]

A. Szameit, Y. V. Kartashov, F. Dreisow, T. Pertsch, S. Nolte, A. Tunnermann, and L. Torner, “Observation of two-dimensional surface solitons in asymmetric waveguide arrays,” Phys. Rev. Lett. 98, 173903 (2007).
[CrossRef]

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Figures (7)

Fig. 1
Fig. 1

Intensity distribution of 1D chirped optical lattices. (a)–(c) Positively chirped optical lattices. (d)–(f) Negatively chirped optical lattices. With a defect at the surface: (a) and (d) positive defect ε = 0.5 ; (b) and (e) zero defect ε = 0 ; (c) and (f) negative defect ε = 0.5 .

Fig. 2
Fig. 2

(Color online) For positive defect with ε = 0.5 , (a) power P versus propagation constant μ. Stable examples: (b),(c) μ = 9.0 [corresponding to point A in (a)].

Fig. 3
Fig. 3

(Color online) For zero defect with ε = 0 , (a) power P versus propagation constant μ. Stable examples: (b),(c) μ = 6.6 (point B).

Fig. 4
Fig. 4

(Color online) For negative defect with ε = 0.5 , (a) power P versus propagation constant μ. (b) Perturbation growth rate versus propagation constant μ. Unstable examples: (c),(d) μ = 8.8 .

Fig. 5
Fig. 5

Stable region (gray shade) for dependences of propagation constant μ on defect parameter ε.

Fig. 6
Fig. 6

(Color online) (a) For defects with ε = 0.9 , 1.0, 1.1, 1.2, and 1.3, stability regions for dependences of power P on propagation constant μ. (b) Perturbation growth rate versus propagation constant μ. (c) Stability (gray shade) and instability (white) regions for dependences of propagation constant μ on defect parameter ε.

Fig. 7
Fig. 7

(Color online) For μ = 6.8 , stable soliton profiles with different defect parameters ε: (a) ε = 0.9 , (c) ε = 1.0 , (e) ε = 1.1 , and (g) ε = 1.2 ; their stable propagations in (b), (d), (f), and (h).

Equations (4)

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i q z = 1 2 2 q x 2 | q | 2 q p R ( x ) q ,
R ( x ) = { 1 cos [ W ( x ) x ] } [ 1 + ε f D ( x ) ] ,
R ( x ) = 0 ,
1 2 2 f x 2 μ f + | f | 2 f + p R ( x ) f = 0.

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